Probability worksheet — GCSE Foundation

1.A factory finds that the probability a randomly chosen light bulb is defective is 0.035. In a batch of 4,000 bulbs, work out how many bulbs you would expect to work correctly.

2.A fair six-sided dice is rolled once. Write down the probability of rolling a 6.

3.A machine makes 4000 light bulbs a day and runs 5 days a week. Two inspectors test bulbs from this machine. Inspector A tests 40 bulbs and finds 4 faulty. Inspector B tests 500 bulbs and finds 30 faulty. Using the better of the two estimates, work out how many faulty bulbs the machine is expected to make in one week.

4.A fair coin is flipped again and again. After the first 10 flips there have been 7 heads. After 1000 flips there have been 528 heads. Which statement best describes what these results show?

5.At a summer fair, the probability of winning at the hoopla stall is 6/10 and the probability of winning at the coconut shy is 2/10. Work out how many times as likely a player is to win at the hoopla stall as at the coconut shy.

6.In a board game Mia moves forward by the total of two ordinary fair dice. Work out the probability that her total is 7. Give your answer as a fraction in its simplest form.

7.A seed company tests germination using results from three greenhouses. Greenhouse 1 plants 200 seeds and 172 germinate. Greenhouse 2 plants 150 seeds and 126 germinate. Greenhouse 3 plants 250 seeds and 212 germinate. Using the combined results from all three greenhouses, work out the best estimate of the number of seeds, out of a new batch of 4000 seeds, that would be expected to germinate.

8.One card is taken at random from an ordinary pack of 52 playing cards. 26 of the cards are red. Work out the probability that the card is red. Give your answer as a percentage.

9.A bag contains one red counter and one blue counter. Josh takes a counter, notes its colour, puts it back, then takes a counter again. He draws a tree diagram to show every possible pair of colours. Work out how many outcomes are on his tree diagram.

10.A spinner is divided into 8 equal sections. 3 of the sections are red and the rest are not red. The spinner is spun once. Work out the probability that it does not land on red.

11.A fair six-sided dice is rolled 90 times. Work out how many more times you would expect it to land on a number less than 4 than on a 6.

12.Two events are independent. The first has probability 2/5 and the second has probability 1/3. Work out the probability that both events happen.

13.180 gardeners at an allotment were asked whether they grow vegetables organically. 100 of the gardeners are on the north plots. 64 of the north-plot gardeners grow organically. 30 of the south-plot gardeners do not grow organically. Work out how many south-plot gardeners grow organically.

14.A fair six-sided dice is rolled 300 times. Work out how many more times you would expect it to land on an even number than on a six.

15.A card is taken at random from an ordinary pack of 52 playing cards. The probability that the card is a diamond is 1/4. Work out the probability that the card is not a diamond.